Take this original string, and let the flag be "01111110" (0-bit stuffing):
0100111110101
After the bit stuffing, the resulting string is the same, but the meaning of the sequence 01111110 is different: it is interpreted as an original flag which has been stuffed.
I know I am wrong, I would like to know where my logic is flawed.
If I am understanding your question correctly then the meaning is completely changed by the context the string is interpreted in (interpreted by different pieces of code) - the happenstance that the original string ends up being a sub-string has no bearing.